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Question
The rate of change of the area of a circle with respect to its radius r at r = 6 cm is (A) 10π (B) 12π (C) 8π (D) 11π
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Solution
The radius of the circle is 6 cm .
Let the radius of circle be r and its area be A .
The volume of the air bubble is given by,
A = π r 2 (1)
Differentiate equation (1) to obtain the rate of change of A with respect to r .
d A d t = d d r π r 2 = 2 π r (2)
According to the given condition,
r = 6 cm
Substitute the value of r in equation (2).
d A d t = 2 π × 6 = 12 π cm 2 / s
Thus, the area of circle is increasing at the rate of 12 π cm 2 / s .
The correct option is B.
The radius of the circle is
Let the radius of circle be
The volume of the air bubble is given by,
Differentiate equation (1) to obtain the rate of change of
According to the given condition,
Substitute the value of
Thus, the area of circle is increasing at the rate of
The correct option is B.
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